1Chapter 3: Numerical Descriptive Measures Some part of chapter 3 has been covered in the lab session of section 2 due to being behind of the schedule. Thus, that part has been provided here since some students did not have pen and paper to take notes in the lab. Quartile Measures Quartiles split the ranked data into 4 segments with an equal number of values per segment The first quartile, Q1, is the value for which 25% of the observations are smaller and 75% are larger Q2 is the same as the median (50% of the observations are smaller and 50% are larger) Only 25% of the observations are greater than the third quartile Find a quartile by determining the value in the appropriate position in the ranked data: First quartile position: Q1 = (n+1)/4 ranked value Second quartile position: Q2 = (n+1)/2ranked value Third quartile position: Q3 = 3(n+1)/4 ranked value , where nis the number of observed values When calculating the ranked position use the following rules: If the result is a whole number then it is the ranked position to use If the result is a fractional half (e.g. 2.5, 7.5, 8.5, etc.) then average the two corresponding data values. If the result is not a whole number or a fractional half then round the result to the nearest integer to find the ranked position. Example:Sample Data in Ordered Array: 11 12 13 16 16 17 18 21 22 Q1 is in the (9+1)/4 = 2.5 position of the ranked data, so Q1 = (12+13)/2 = 12.5Q1 Q2 Q3 25% 25% 25% 25%

This preview
has intentionally blurred sections.
Sign up to view the full version.